FINITE GROUPS WITH THE SAME CONJUGACY CLASS SIZES AS A FINITE SIMPLE GROUP

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AHANJIDEH NEDA

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ISSN: 2588-4824

Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2019 | Volume:8 | Issue:1 Page(s): 23-33

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Title

FINITE GROUPS WITH THE SAME CONJUGACY CLASS SIZES AS A FINITE SIMPLE GROUP

Author(s)

AHANJIDEH NEDA | Issue Writer Certificate

Keywords

Prime graph

the set of the order components of a nite group

the Schur multiplier

Abstract

For a nite group H, let cs(H) denote the set of non-trivial conjugacy class sizes of H and OC(H) be the set of the order components of H. In this paper, we show that if S is a nite simple group with the disconnected Prime graph and G is a nite group such that cs(S) = cs(G), then jSj = jG=Z(G)j and OC(S) = OC(G=Z(G)). In particular, we show that for some nite simple group S, G = S Z(G).

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APA: Copy

AHANJIDEH, NEDA. (2019). FINITE GROUPS WITH THE SAME CONJUGACY CLASS SIZES AS A FINITE SIMPLE GROUP. INTERNATIONAL JOURNAL OF GROUP THEORY, 8(1), 23-33. SID. https://sid.ir/paper/723638/en

Vancouver: Copy

AHANJIDEH NEDA. FINITE GROUPS WITH THE SAME CONJUGACY CLASS SIZES AS A FINITE SIMPLE GROUP. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2019;8(1):23-33. Available from: https://sid.ir/paper/723638/en

IEEE: Copy

NEDA AHANJIDEH, “FINITE GROUPS WITH THE SAME CONJUGACY CLASS SIZES AS A FINITE SIMPLE GROUP,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 8, no. 1, pp. 23–33, 2019, [Online]. Available: https://sid.ir/paper/723638/en

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